48,406 research outputs found
Bayesian Learning-Based Adaptive Control for Safety Critical Systems
Deep learning has enjoyed much recent success, and applying state-of-the-art
model learning methods to controls is an exciting prospect. However, there is a
strong reluctance to use these methods on safety-critical systems, which have
constraints on safety, stability, and real-time performance. We propose a
framework which satisfies these constraints while allowing the use of deep
neural networks for learning model uncertainties. Central to our method is the
use of Bayesian model learning, which provides an avenue for maintaining
appropriate degrees of caution in the face of the unknown. In the proposed
approach, we develop an adaptive control framework leveraging the theory of
stochastic CLFs (Control Lyapunov Functions) and stochastic CBFs (Control
Barrier Functions) along with tractable Bayesian model learning via Gaussian
Processes or Bayesian neural networks. Under reasonable assumptions, we
guarantee stability and safety while adapting to unknown dynamics with
probability 1. We demonstrate this architecture for high-speed terrestrial
mobility targeting potential applications in safety-critical high-speed Mars
rover missions.Comment: Corrected an error in section II, where previously the problem was
introduced in a non-stochastic setting and wrongly assumed the solution to an
ODE with Gaussian distributed parametric uncertainty was equivalent to an SDE
with a learned diffusion term. See Lew, T et al. "On the Problem of
Reformulating Systems with Uncertain Dynamics as a Stochastic Differential
Equation
Dynamics of Social Networks: Multi-agent Information Fusion, Anticipatory Decision Making and Polling
This paper surveys mathematical models, structural results and algorithms in
controlled sensing with social learning in social networks.
Part 1, namely Bayesian Social Learning with Controlled Sensing addresses the
following questions: How does risk averse behavior in social learning affect
quickest change detection? How can information fusion be priced? How is the
convergence rate of state estimation affected by social learning? The aim is to
develop and extend structural results in stochastic control and Bayesian
estimation to answer these questions. Such structural results yield fundamental
bounds on the optimal performance, give insight into what parameters affect the
optimal policies, and yield computationally efficient algorithms.
Part 2, namely, Multi-agent Information Fusion with Behavioral Economics
Constraints generalizes Part 1. The agents exhibit sophisticated decision
making in a behavioral economics sense; namely the agents make anticipatory
decisions (thus the decision strategies are time inconsistent and interpreted
as subgame Bayesian Nash equilibria).
Part 3, namely {\em Interactive Sensing in Large Networks}, addresses the
following questions: How to track the degree distribution of an infinite random
graph with dynamics (via a stochastic approximation on a Hilbert space)? How
can the infected degree distribution of a Markov modulated power law network
and its mean field dynamics be tracked via Bayesian filtering given incomplete
information obtained by sampling the network? We also briefly discuss how the
glass ceiling effect emerges in social networks.
Part 4, namely \emph{Efficient Network Polling} deals with polling in large
scale social networks. In such networks, only a fraction of nodes can be polled
to determine their decisions. Which nodes should be polled to achieve a
statistically accurate estimates
Bayesian Over-the-Air FedAvg via Channel Driven Stochastic Gradient Langevin Dynamics
The recent development of scalable Bayesian inference methods has renewed
interest in the adoption of Bayesian learning as an alternative to conventional
frequentist learning that offers improved model calibration via uncertainty
quantification. Recently, federated averaging Langevin dynamics (FALD) was
introduced as a variant of federated averaging that can efficiently implement
distributed Bayesian learning in the presence of noiseless communications. In
this paper, we propose wireless FALD (WFALD), a novel protocol that realizes
FALD in wireless systems by integrating over-the-air computation and
channel-driven sampling for Monte Carlo updates. Unlike prior work on wireless
Bayesian learning, WFALD enables (\emph{i}) multiple local updates between
communication rounds; and (\emph{ii}) stochastic gradients computed by
mini-batch. A convergence analysis is presented in terms of the 2-Wasserstein
distance between the samples produced by WFALD and the targeted global
posterior distribution. Analysis and experiments show that, when the
signal-to-noise ratio is sufficiently large, channel noise can be fully
repurposed for Monte Carlo sampling, thus entailing no loss in performance.Comment: 6 pages, 4 figures, 26 references, submitte
Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks
Effective training of deep neural networks suffers from two main issues. The
first is that the parameter spaces of these models exhibit pathological
curvature. Recent methods address this problem by using adaptive
preconditioning for Stochastic Gradient Descent (SGD). These methods improve
convergence by adapting to the local geometry of parameter space. A second
issue is overfitting, which is typically addressed by early stopping. However,
recent work has demonstrated that Bayesian model averaging mitigates this
problem. The posterior can be sampled by using Stochastic Gradient Langevin
Dynamics (SGLD). However, the rapidly changing curvature renders default SGLD
methods inefficient. Here, we propose combining adaptive preconditioners with
SGLD. In support of this idea, we give theoretical properties on asymptotic
convergence and predictive risk. We also provide empirical results for Logistic
Regression, Feedforward Neural Nets, and Convolutional Neural Nets,
demonstrating that our preconditioned SGLD method gives state-of-the-art
performance on these models.Comment: AAAI 201
Stochastic Gradient Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for
defining distant proposals with high acceptance probabilities in a
Metropolis-Hastings framework, enabling more efficient exploration of the state
space than standard random-walk proposals. The popularity of such methods has
grown significantly in recent years. However, a limitation of HMC methods is
the required gradient computation for simulation of the Hamiltonian dynamical
system-such computation is infeasible in problems involving a large sample size
or streaming data. Instead, we must rely on a noisy gradient estimate computed
from a subset of the data. In this paper, we explore the properties of such a
stochastic gradient HMC approach. Surprisingly, the natural implementation of
the stochastic approximation can be arbitrarily bad. To address this problem we
introduce a variant that uses second-order Langevin dynamics with a friction
term that counteracts the effects of the noisy gradient, maintaining the
desired target distribution as the invariant distribution. Results on simulated
data validate our theory. We also provide an application of our methods to a
classification task using neural networks and to online Bayesian matrix
factorization.Comment: ICML 2014 versio
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